On the periodic and asymptotically periodic nonlinear Helmholtz equation. (March 2017)

• Record Type: Journal Article
• Authors: Evéquoz, Gilles
• Is Part Of: Nonlinear analysis. Volume 152(2017)
• Page Start: 88
• Page End: 101
• Publication Date: 2017-03
• Subjects: 35J20 -- 35J05; Nonlinear Helmholtz equation -- Variational method -- Pseudo-gradient flow; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.12.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In the first part of this paper, the existence of infinitely many L p -standing wave solutions for the nonlinear Helmholtz equation − Δ u − λ u = Q ( x ) ∣ u ∣ p − 2 u in R N is proven for N ≥ 2 and λ > 0, under the assumption that Q be a nonnegative, periodic and bounded function and the exponent p lies in the Helmholtz subcritical range. In a second part, the existence of a nontrivial solution is shown in the case where the coefficient Q is only asymptotically periodic.